Which of the following numbers is a multiple of 4? ${70,76,89,105,110}$
Explanation: The multiples of $4$ are $4$ $8$ $12$ $16$ ..... In general, any number that leaves no remainder when divided by $4$ is considered a multiple of $4$ We can start by dividing each of our answer choices by $4$ $70 \div 4 = 17\text{ R }2$ $76 \div 4 = 19$ $89 \div 4 = 22\text{ R }1$ $105 \div 4 = 26\text{ R }1$ $110 \div 4 = 27\text{ R }2$ The only answer choice that leaves no remainder after the division is $76$ $ 19$ $4$ $76$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $76$ $76 = 2\times2\times19 4 = 2\times2$ Therefore the only multiple of $4$ out of our choices is $76$. We can say that $76$ is divisible by $4$.